Valeant Pharmaceuticals International Inc. CEO Michael Pearson said the company is nearing its goal of rounding up enough support from Allergan Inc. shareholders to secure a vote on its $53 billion hostile bid for the Botox maker.

Once Valeant gets the 25% of Allergan shareholders needed to convene the vote, "both sides know how this will come out," Mr. Pearson said in an interview Tuesday, adding that he expects Valeant's...